2 problems

For $q\in[0,1]$, call a graph $J$ $q$-sparse if … where $\mathbb{E}_qX_I$ is the expected number of copies of $I$ in $G_{n,q}$. Sparse-graph reformulation. There is a fixed $K$ suc…

For a graph $H$, let $\mathbb{E}_pX_I$ denote the expected number of copies of $I$ in $G_{n,p}$, and define the fractional expectation threshold by … where $N(H,I)$ is the number o…